A process for treating a semiconductor wafer such as a silicon wafer includes controlling an in-plane temperature distribution of the silicon wafer as desired while controlling a temperature of the silicon wafer to a temperature setpoint.
For this purpose, there has been known a method of controlling the temperature of the semiconductor wafer simultaneously using a plurality of temperature adjusters through control loops respectively provided to the temperature adjusters.
As such a control method in a multi-input multi-output system, a model following servo control system has been known (see, for instance, Patent Literature 1: JP-A-2009-173969).
In the model following servo control system, a model (e.g., second-order lag system) having dynamic characteristics desirable as a reference model is generally selected.
Accordingly, in setpoint response, a control variable follows a step response of the model as a reference trajectory.
When a manipulated variable has upper and lower limits (saturation), the model is selected so that the maximum speed is obtainable preferably in a range where the manipulated variable does not reach the saturation. On the other hand, in order to improve throughput in the process, it is desirable to intentionally bring the manipulated variable to saturation to reach the setpoint at the highest speed in the shortest time of period.
However, in a heating plate having multiple zones (multi-input multi-output system) as described in Patent Literature 1, heating at the saturation level of the manipulated variable deteriorates temperature uniformity between the zones since the zone heated at the slowest speed is delayed from the other zones in a temperature increasing speed.